I don’t think we should invoke supernatural miracles where it is not warranted – that is something that YECs are compelled to do extensively with their interpretations.
I have no hypernatural explanation for axe heads floating, although there might be one, but I am quite comfortable with a hypernatural explanation for Joshua’s long day, related here. It in no way diminishes God’s sovereignty over his creation – in fact, hypernatural explanations exalt it, because they involve precursor events and God’s sovereignty over time.